Mathematical modelling of food blenders

Have you ever forgotten to replace the lid of the blender before beginning to puree your mango and passion-fruit smoothie? If you have, you'll have witnessed the catastrophic explosion of fruit and yoghurt flung haphazardly around the kitchen, stretching to the furthermost points in an unpredictable manner. This is consequential of the complicated and turbulent fluid dynamics present within the machine, the exact behaviour of which is unknown. Sharp, angular blades rotate at extremely high speeds to mix and chop the fruit into a puree of particles that are as small and uniform in size as possible. But what characteristics of the blender are responsible for the outcome? While experimental evidence gives intuition into blade and vessel design, along with operational parameters such as speed and blend time, there is a knowledge gap surrounding the precise impact on the particle and fluid dynamics. How interdependent are the chopping and mixing mechanisms? What determines the minimum particle size and how can it be lowered?

This seemingly simple, user-friendly appliance is governed by complex and captivating mathematics. Caoimhe Rooney focused on understanding the particle and fluid dynamics involved in the blending process. By deriving a system of integral ordinary differential equations inspired by Becker-Döring theory, we can obtain a predictive model that allows us to study the resulting particle size distribution of a smoothie. The result: knowledge of the precise operating regime that will create the finest, most homogeneous purees in the most efficient manner.



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A Ninja blender.